In cubic and near-cubic ionic and semiconducting compounds, we can fin
d two correlationships among the optical dielectric constant epsilon(i
nfinity), short-range and long-range forces. In the relationships, the
chemical valence of high ionic conductors takes the value shifted fro
m the formal value. The shift can be explained from the effect of d-el
ectron energy level near the band gap. A linear relationship of In (ep
silon(infinity)) to ln (T(c)) is found for fast-ionic conductors. From
these relations, intimate correlation of the band gap energy to the f
ast-ionic conduction is suggested.